Many-body physics with individually controlled Rydberg atoms

Recent decades have witnessed great developments in the field of quantum simulation—where synthetic systems are built and studied to gain insight into complicated, many-body real-world problems. Systems of individually controlled neutral atoms, interacting with each other when excited to Rydberg states, have emerged as a promising platform for this task, particularly for the simulation of spin systems. Here, we review the techniques necessary for the manipulation of neutral atoms for the purpose of quantum simulation—such as quantum gas microscopes and arrays of optical tweezers—and explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models. We discuss recent achievements in the study of quantum many-body physics in this platform, and some current research directions beyond that.